A control system framework for privacy preserving demand response of thermal inertial loads

Abstract

We address a problem in demand response for the class of thermal inertial loads: How to control the total demand of a set of loads, and also what to control it to, all while respecting constraints on load states, as well as maintaining privacy of load states. The architecture we investigate consists of an aggregator or Load Serving Entity (LSE) serving several thermostatically controlled loads (TCLs), whose set-points are controlled by the LSE to follow a desired total power consumption. We propose a modeling, analysis and design framework for the LSE that accomplishes this goal by solving a hierarchy of two control problems. The first control problem consists of determining an optimal aggregate power trajectory given the price forecasts. The second problem is that of controlling the set-points of the TCL population so as to drive their total power consumption to follow the optimal power trajectory. We show how the LSE can solve these control problems while guaranteeing privacy and contractual comfort bounds for the TCL states. Numerical simulations illustrate the efficacy of the proposed framework.

Optimal power consumption for demand response of thermostatically controlled loads

“…24 On the other hand, a linear program (LP) relaxation of the MILP, resulting from the control convexification u i ∈ {0, 1}  →ũ i ∈ [0, 1], has much faster runtime and was reported in our earlier work. 17 Furthermore, the optimal solution of the LP relaxation has the physical meaning of average ON duration over a discretization interval (see Figure 3). However, the MILP equality constraint does not satisfy total unimodularity (see, for example, chapter 5 in the work of Schrijver 25 ); consequently, the optimal solution of the LP relaxation is not the optimal solution of the MILP.…”

A tractable formulation for multi-period linearized optimal power flow in presence of thermostatically controlled loads

“…However, it could be argued that such a model of the control action is not fully coherent with the underlying probabilistic model for the system. Other authors have proposed a control action based on modifying the deadband in which the TCL does not switch, for instance [12] and [13]. Recently, a different control paradigm based on energy packets inspired from communication systems has been proposed in [14].…”

Optimal Control of Thermostatic Loads for Planning Aggregate Consumption: Characterization of Solution and Explicit Strategies

“…, consider the control values (u i , u i ) as in (12). The optimal control for problem (P) satisfies…”

“…Thermostatically controlled loads (TCLs), such as air conditioners (ACs), are valuable as flexible resources to elicit demand response, i.e., for actively controlling the loads to offset intermittency in the generation side (e.g., due to renewables) [1], [2], [11], [12], [15]. Utilities or load serving entities (LSEs) can dynamically exploit the thermal inertia of the population of TCLs to strategically plan and control the aggregate consumption in a desired manner.…”